Related papers: The $\Phi_3^4$ measure has sub-Gaussian tails
In this paper, we obtain a refined non-asymptotic tail bound for the largest singular value (the soft edge) of sub-Gaussian matrix. As an application, we use the obtained theorem to compute the tail bound of the Gaussian Toeplitz matrix.
We show, both analytically and numerically, that non-Gaussian tails in the probability density function of curvature perturbations arise in ultra-slow-roll inflation from the $\delta N$ formalism, without invoking stochastic inflation.…
We present a simple alternative to the Crystal Ball function that has an exponential tail stitched to a Gaussian core. It has one parameter less than the Crystal Ball function and, where appropriate, offers more stable fits to peaks that…
We constructed in a previous work the $\Phi^4_3$ measures on compact boundaryless $3$-dimensional Riemannian manifolds as some invariant probability measures of some Markovian dynamics. We prove in the present work that these dynamics have…
Expectile, as the minimizer of an asymmetric quadratic loss function, is a coherent risk measure and is helpful to use more information about the distribution of the considered risk. In this paper, we propose a new risk measure by replacing…
The q-Gaussians are a class of stable distributions which are present in many scientific fields, and that behave as heavy tailed distributions for an especific range of q values. The identification of these values, which are used in the…
Extending Gross's result, we prove that a certain factorizaton of measures holds for all $p$ and any finite even Dirichlet character $\chi$ of any conductor, rather than only for split $p$ and $\chi$ with conductor a power of $p$. Using…
We consider time-dependent singular stochastic partial differential equations on the three-dimensional torus. These equations are only well-posed after one adds renormalization terms. In order to construct a well-defined notion of solution,…
We show bounds on tail probabilities for quadratic forms in sub-gaussian non-necessarily independent random variables. Our main tool will be estimates of the Luxemburg norms of such forms. This will allow us to formulate the above-mentioned…
Gaussian random vectors exhibit the loss of dimension phenomena, which relate to their joint survival tail behaviour. Besides, the fact that the components of such vectors are light-tailed complicates the approximations of various…
We consider the tail behavior of random variables $R$ which are solutions of the distributional equation $R\stackrel{d}{=}Q+MR$, where $(Q,M)$ is independent of $R$ and $|M|\le 1$. Goldie and Gr\"{u}bel showed that the tails of $R$ are no…
We propose and analyze a new estimator of the covariance matrix that admits strong theoretical guarantees under weak assumptions on the underlying distribution, such as existence of moments of only low order. While estimation of covariance…
We show almost sure wellposedness of mild solution to the cubic nonlinear wave equation in a weighted Besov space over $\mathbb R^2$. To achieve this, we show that any weak limit of $\phi^4$ measures on increasing tori is invariant under…
In previous work Majda and McLaughlin computed explicit expressions for the $2N$th moments of a passive scalar advected by a linear shear flow in the form of an integral over ${\bf R}^N$. In this paper we first compute the asymptotics of…
The exact expression for the probability density $p_{_N}(x)$ for sums of a finite number $N$ of random independent terms is obtained. It is shown that the very tail of $p_{_N}(x)$ has a Gaussian form if and only if all the random terms are…
We consider the fractional $\Phi^3_d$-measure on the $d$-dimensional torus, with Gaussian free field having inverse covariance $(1-\Delta)^\alpha$, and show a phase transition at $d=3\alpha$. More precisely, in a regular regime $d<3\alpha$,…
The primary quantum mechanical equation of motion entails that measurements typically do not have determinate outcomes, but result in superpositions of all possible outcomes. Dynamical collapse theories (e.g. GRW) supplement this equation…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…
Under certain regularity conditions, we establish quasi-invariance of Gaussian measures on periodic functions under the flow of cubic fractional nonlinear Schr\"{o}dinger equations on the one-dimensional torus.
Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…